By using transfer matrices method a computation has been carried out on the axial field distribution and the optical properties of the electrostatic quadrupole lens of different electrode shapes such as, cylindrical convex and spherical electrodes.The path of charged–particles beam traversing the field model has been determined by solving the trajectory equation of motion in Cartesian coordinates. The optical properties of the electrostatic quadrupole lens have been computed with the aid of the beam trajectory along the lens axis. Optimization calculations have been conducted to determine the most favorable optical properties and the design specifications of an electrode shape of quadrupole lens. The computations have been mainly concentrated on determining the electrode shape parameters, excitation, the focal lengths, magnification and aberration parameters in both horizontal and vertical planes of the trajectory along the optical axis for each design.The optimization calculations are made to find the optimum values of spherical and chromatic aberration coefficients by changing the geometrical shapes of electrodes via taking the different gap angles of electrode into account. The results show that the choice of the given range of geometrical dimension such as the range of gap angle or electrode radius to aperture radius ratio give us the optimum optical properties and the best values of aberration coefficients.
